Big plus +1 for the Pioneer SP-BS22-LR. Eventually paired with one then two SVS subwoofers in your budget range should serve you nicely until you hit the Lotto.
I assembled two Pioneer BS22 7.1 HT systems for friends, one using two SVS SB-1000's and another with two Velodyne DD-10 Plus. Since they budgeted on the DD's they planned on upgrading the Pioneers. That was over two years ago.
While not in your budget my ownership with the then top of the line Paradigm Studio 100 v1, v2 and S8's I cannot recommended brand.
There are some other good suggestions here you should take a hard look at.
Welcome to the Mob.